its easy

Geometry Level 2

if a right angled triangle has side lengths a,b and c such that c is hypotenuse and $c\quad =\sqrt [ 2 ]{ 2ab }$ find the smallest angle of the triangle?

The answer is 45.

2 solutions

Rifath Rahman
Aug 13, 2014

c=sqrt 2ab or c^2=(sqrt 2ab)^2 or c^2=2ab or a^2+b^2=2ab or a^2-2ab+b^2=0 or (a-b)^2=0 or (a-b)=0 or a=b.So its an isosceles right triangle.That means angles are 90,45,45.So the smallest angle is/are 45

George Chen
Aug 3, 2014

√(a²+b²)=√(ab), a²+b²=ab, and a,b>0, therefore a,b=1. It is a right isosceles triangle that has angles of 45°, 45°, and 90°.

Both $a, b$ need not be $1$ . We have $a = b$ .

Here's why. From $a^2 + b^2= 2ab,$ we get a nice factorization, giving us $a = b$ . You dropped a 2.

Sean Roberson - 6 years, 10 months ago

Thanks for pointing out the mistakes.

George Chen - 6 years, 10 months ago

its easy

The answer is 45.

2 solutions

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